3.1 History of Representation of 4D Structures in Space and Time

To describe the representation of natural phenomena as 4D structures I will summarise the history of representation of space and time. Visual representation of structures in space preceded studies of time-related changes of those structures. Accurate drawings of human anatomy were well developed in the Renaissance. Conversely, changes of physical events in time were initially recorded as tables of values at various time points, as in a modern spreadsheet. Then a cognitive revolution of ‘visual thinking’ led to graphic representation of events over time. This approach made physical phenomena visualisable in the form of geographical maps, scatter plots, and eventually graphic traces of physical events. By revealing elements that would otherwise remain invisible, data visualisation had a profound effect on the way we approach problems¹.

The graphic representation of physical events already had a history of revealing previously undetected phenomena. An initial development of this began as early as the mid-seventeenth century, with the invention of the barometer. In 1684, Robert Plot used barometers to display daily changes in barometric pressure in a graph he called a “History of the Weather”². Since then, the discipline of meteorology benefited with multiple graphic recording with thermometers barometers, hygrometers and the measurement of rainfall and wind.

In 1796, Joseph-Louis Lagrange described mechanical dynamics as a geometry in four dimensions.³ At the beginning of the nineteenth century, there was increasing emphasis on objective, measurable events that could be shared between observers⁴. This was an intellectual rebellion against the ‘Philosophy of Nature’ (Naturphilosophie), which assumed a ‘vital force’ to explain biological phenomena⁵.

However, it was only in 1847 when Carl Ludwig, invented the Kymograph, a rotating smoked drum⁶, becoming the first method to transform visual observations and numerical measurements into a graphic record. Kymographic images recorded the movements of muscles as a continuous trace, freezing them in time and allowing closer examination of the ‘character and extent’ of the event.

Other researchers quickly recognised the tremendous potential of Ludwig’s method. For example, Emil du Bois-Reymond only a year later commented that “the dependence of the effects upon each condition is now presented in the form of a curve, whose exact law, to be sure, remains unknown, but whose general character one will most often be able to trace. It will almost always be possible to determine whether the function grows or diminishes with the variable investigated. In other cases, one may be able to discover distinctive points of the curves, the sense of its bending with respect of the abscissa, or whether it approaches asymptotically a constant value…”⁷. Soon after, Volkmann added that “After Ludwig invented an instrument that permitted one to represent the variable forces of the heart through curves, it immediately suggested making other motive forces also visualisable and measurable…”⁸. 

The smoked drum was followed in the 20^th century first by the polygraph, an electronic version of the smoked drum⁹ with allows several parameters to be recorded simultaneously in the same time frame, and more recently by computers with sophisticated data acquisition software. I am probably one of the few researchers who used all three methods!

The graphic representation of changes of a physical parameter over time represents the beginning of modern science and is in common use now in all disciplines. Interestingly, the need to visualise physical events as more than just mathematical theories, was proposed by Werner Heisenberg in 1927 when he stressed that picturability (Auschaulichkeit) is a proper goal of physical theory, one requisite for physical understanding¹⁰.

As Andrienco and colleagues summarised well in 2003: “Modern computer technologies provide better than ever before opportunities for storage, management, visualization, and analysis of dynamic, i.e. temporally variable, data, including dynamic spatial data (further referred to as spatio-temporal data).”¹¹

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1. Michael Friendly & Howard Wainer (2021): A History of Data Visualization and Graphic Communication. Harvard University Press. ↩︎
2. For more, see: https://en.wikisource.org/wiki/Dictionary_of_National_Biography,_1885-1900/Plot,_Robert
   https://www.tandfonline.com/doi/abs/10.1080/26375451.2023.2224132 ↩︎
3. J-L Lagrange (1796): Theorie des fonctions analytiques. Imprimerie de la Republique, chapter 1, note 19. ↩︎
4. Hebbel E Hoff & LA Geddes (1962): The Beginnings of Graphic Recording. Isis 53(3) 287-324;
   Merriley Borell 1987): Instrumentation and the Rise of Modern Physiology. Science & Technology Studies 5(2) 53-62. ↩︎
5. Erich Bauereisen (1962): Carl Ludwig As The Founder Of Modern Physiology. The Physiologist 4, 293-299. ↩︎
6. Carl Ludwig (1847): Beiträge zur Kenntniss des Einflusses der Respirationsbewegungen auf den Blutlauf im Aortensysteme. Archiv für Anatomie, Physiologie und wissenschaftliche Medicin: 242- 302 ↩︎
7. Emil du Bois-Reymond (1848-1884): Untersuchungen über tierische Elektricität / Researches on Animal Electricity.
   For more on du Bois-Reymond, see: https://thereader.mitpress.mit.edu/the-greatest-unknown-intellectual-of-the-19th-century/ ↩︎
8. Alfred Wilhelm Volkmann (1850): Die Hämodynamik nach Versuchen. Breitkopf und Härtel. ↩︎
9. The ‘polygraph’ lie detector test uses these machines to measure various physiological parameters. But their efficacy at detecting lies has not been supported by evidence. See: https://en.wikipedia.org/wiki/Polygraph ↩︎
10. The term appears in Heisenberg’s classic paper on the celebrated uncertainty principle: Werner Heisenberg (1927): Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik 43, 172–198. ↩︎
11. Natalia Andrienko, Gennady Andrienko & Peter Gatalsky (2003): Exploratory spatio-temporal visualization: an analytical review. Journal of Visual Languages & Computing 14(6) 503-541. ↩︎

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